A fuel cell system is known in the art, which includes a fuel cell stack configured to generate electric power by an electrochemical reaction of a fuel gas and an oxidant gas, a radiator configured to lower a temperature of cooling water for the fuel cell stack, a cooling water feed passage connecting an outlet of a radiator inside cooling water passage in the radiator and an inlet of a stack inside cooling water passage in the fuel cell stack together, the cooling water feed passage including a feed side branching point, a radiator outflow passage from the outlet of the radiator inside cooling water passage to the feed side branching point and a stack inflow passage from the feed side branching point to the inlet of the stack inside cooling water passage, a cooling water discharge passage connecting an outlet of the stack inside cooling water passage and an inlet of the radiator inside cooling water passage, the cooling water discharge passage including a discharge side branching point, a stack outflow passage from the outlet of the stack inside cooling water passage to the discharge side branching point, and a radiator inflow passage from the discharge side branching point to the inlet of the radiator inside cooling water passage, a bypass cooling water passage connecting the feed side branching point and the discharge side branching point together, the bypass cooling water passage including a deionizer configured to remove ions in the cooling water, a cooling water pump arranged in the radiator outflow passage so that an inlet thereof faces the radiator, and a bypass cooling water control valve controlling an amount of cooling water flowing through the bypass cooling water passage, in which the cooling water pump is driven and the bypass cooling water control valve is controlled so that part of the cooling water having flowed through the radiator outflow passage flows through the bypass cooling water passage and the remainder flows through the stack inside cooling water passage of the fuel cell stack (for example, see PLT 1). Ions are eluted into the cooling water from the radiator etc. As a result, an electrical conductivity of the cooling water increases. In this regard, if cooling water with an excessively high electrical conductivity flows into the fuel cell stack, the fuel cell stack is liable to fall in electrical insulating ability. In the fuel cell system of PLT 1, part of the cooling water always flows through the deionizer and, thus, the cooling water is lowered in electrical conductivity. Therefore, the ability to electrically insulate the fuel cell stack is less reduced. Note that, in the fuel cell system of PLT 1, the remaining cooling water always flows through the fuel cell stack.